A search and rescue aircraft, travelling at a speed of 240 km/h starts out at a heading of N 20 degrees West. After travelling for 1h and 15 min, it turns to a heading of N 80 degrees E and continues for another two hours before returning to base. Find the total distance the aircraft travelled and how long it took.
240 * 1.25 = 300 @ N20W = <-102.6,281.9>
240 * 2.00 = 480 @ N80E = <472.7,83.4>
add 'em up to get <370.1,315.3>
So, the distance back is 486.2
300+480+486.2 = 1266.2 km at 240 km/hr = 5.3 hours
To find the total distance traveled by the aircraft, we will break down the journey into different segments and calculate the distance traveled in each segment.
1. Calculate the distance traveled in the first segment:
- Speed: 240 km/h
- Time: 1 hour and 15 minutes = 1.25 hours
- Distance = Speed x Time = 240 km/h x 1.25 h = 300 km
2. Calculate the distance traveled in the second segment:
- Speed: 240 km/h
- Time: 2 hours
- Distance = Speed x Time = 240 km/h x 2 h = 480 km
3. Calculate the distance traveled in the third segment (returning to base):
Since the aircraft is returning to the base, the distance will be the same as the distance in the second segment:
- Distance = 480 km
4. Calculate the total distance traveled:
- Total distance = Distance in segment 1 + Distance in segment 2 + Distance in segment 3
- Total distance = 300 km + 480 km + 480 km = 1260 km
Now, let's calculate the total time taken:
1. Time taken in the first segment: 1 hour and 15 minutes = 1.25 hours
2. Time taken in the second segment: 2 hours
3. Time taken in the third segment (returning to base): Since the aircraft is returning to the base, the time taken will be the same as the time taken in the second segment:
- Time taken = 2 hours
4. Calculate the total time taken:
- Total time taken = Time taken in segment 1 + Time taken in segment 2 + Time taken in segment 3
- Total time taken = 1.25 hours + 2 hours + 2 hours = 5.25 hours
Therefore, the total distance traveled by the aircraft is 1260 km and it took 5.25 hours.
To solve this problem, we can break it down into smaller parts and calculate the distance and time for each segment.
Step 1: Calculate the distance and time traveled in the first segment.
The aircraft travels for 1 hour and 15 minutes at a speed of 240 km/h.
Since we have the time in minutes, we need to convert it into hours:
1 hour + 15 minutes = 1.25 hours
Distance traveled in the first segment = Speed × Time = 240 km/h × 1.25 h = 300 km
Step 2: Calculate the distance and time traveled in the second segment.
The aircraft travels for 2 hours at the same speed.
Distance traveled in the second segment = Speed × Time = 240 km/h × 2 h = 480 km
Step 3: Calculate the distance of the return journey.
Since the aircraft is returning to the base, the distance is the same as the total distance traveled in the first and second segments.
Distance traveled in the return journey = Distance of the first segment + Distance of the second segment = 300 km + 480 km = 780 km
Step 4: Calculate the total distance traveled.
Total distance traveled = Distance of the first segment + Distance of the second segment + Distance of the return journey = 300 km + 480 km + 780 km = 1560 km
Step 5: Calculate the total time taken.
To calculate the total time, we add up the time taken for each segment.
Total time taken = Time taken in the first segment + Time taken in the second segment + Time taken in the return journey = 1.25 h + 2 h + 2 h = 5.25 hours
Therefore, the total distance traveled by the aircraft is 1560 km, and it took 5.25 hours.